Contemporary Mathematics, Volume: 640
2015; 197 pp; softcover
ISBN-13: 978-1-4704-0989-0
This volume contains the proceedings of the Conference on Spectral Theory and Partial Differential Equations, held from June 17-21, 2013, at the University of California, Los Angeles, California, in honor of James Ralston's 70th Birthday.
Papers in this volume cover important topics in spectral theory and partial differential equations such as inverse problems, both analytical and algebraic; minimal partitions and Pleijel's Theorem; spectral theory for a model in Quantum Field Theory; and beams on Zoll manifolds.
Graduate students and research mathematicians interested in spectral theory, mathematical physics, inverse problems, analysis, PDEs, and functional analysis.
Contemporary Mathematics, Volume: 641
2015; 166 pp; softcover
ISBN-13: 978-1-4704-1013-1
This volume contains the proceedings of the WIT: Women in Topology workshop, held from August 18-23, 2013, at the Banff International Research Station, Banff, Alberta, Canada. The Women in Topology workshop was devoted primarily to active collaboration by teams of five to seven participants, each including senior and junior researchers, as well as graduate students.
This volume contains papers based on the results obtained by team projects in homotopy theory, including A-infinity structures, equivariant homotopy theory, functor calculus, model categories, orbispaces, and topological Hochschild homology.
Graduate students and research mathematicians interested in homotopy theory and operads.
Hindustan Book Agency
2015; 110 pp; softcover
ISBN-13: 978-93-80250-74-8
Expected publication date is July 22, 2015.
This book's principal goals are: (i) to present the spectral theorem as a statement on the existence of a unique continuous and measurable functional calculus, (ii) to present a proof without digressing into a course on the Gelfand theory of commutative Banach algebras, (iii) to introduce the reader to the basic facts concerning the various von Neumann-Schatten ideals, the compact operators, the trace-class operators and all bounded operators, and finally, (iv) to serve as a primer on the theory of bounded linear operators on separable Hilbert space.
Students and research mathematicians interested in Hilbert Space.
Hilbert space
The spectral theorem
Beyond normal operators
Appendix
Bibliography
Index
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Mathematical Surveys and Monographs, Volume: 203
2015; 311 pp; hardcover
ISBN-13: 978-1-4704-2197-7
Expected publication date is July 9, 2015.
PROPs and their variants are extremely general and powerful machines that encode operations with multiple inputs and multiple outputs. In this respect PROPs can be viewed as generalizations of operads that would allow only a single output. Variants of PROPs are important in several mathematical fields, including string topology, topological conformal field theory, homotopical algebra, deformation theory, Poisson geometry, and graph cohomology. The purpose of this monograph is to develop, in full technical detail, a unifying object called a generalized PROP. Then with an appropriate choice of pasting scheme, one recovers (colored versions of) dioperads, half-PROPs, (wheeled) operads, (wheeled) properads, and (wheeled) PROPs.
Here the fundamental operation of graph substitution is studied in complete detail for the first time, including all exceptional edges and loops as examples of a new definition of wheeled graphs. A notion of generators and relations is proposed which allows one to build all of the graphs in a given pasting scheme from a small set of basic graphs using graph substitution. This provides information at the level of generalized PROPs, but also at the levels of algebras and of modules over them. Working in the general context of a symmetric monoidal category, the theory applies for both topological spaces and chain complexes in characteristic zero.
This book is useful for all mathematicians and mathematical physicists who want to learn this new powerful technique.
Graduate students and research mathematicians interested in algebraic geometry, algebraic topology, and category theory.
Mathematical Surveys and Monographs, Volume: 204
2015; 536 pp; hardcover
ISBN-13: 978-1-4704-2214-1
Expected publication date is July 30, 2015
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields.
The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric varieties via the notion of a quasitoric manifold. Discovery of remarkable geometric structures on moment-angle manifolds led to important connections with classical and modern areas of symplectic, Lagrangian, and non-Kaehler complex geometry. A related categorical construction of moment-angle complexes and polyhedral products provides for a universal framework for many fundamental constructions of homotopical topology. The study of polyhedral products is now evolving into a separate subject of homotopy theory. A new perspective on torus actions has also contributed to the development of classical areas of algebraic topology, such as complex cobordism.
This book includes many open problems and is addressed to experts interested in new ideas linking all the subjects involved, as well as to graduate students and young researchers ready to enter this beautiful new area.
Graduate students and research mathematicians interested in algebraic topology.
Geometry and combinatorics of polytopes
Combinatorial structures
Combinatorial algebra of face rings
Moment-angle complexes
Toric varieties and manifolds
Geometric structures on moment-angle manifolds
Half-dimensional torus actions
Homotopy theory of polyhedral products
Torus actions and complex cobordism
Commutative and homological algebra
Algebraic topology
Categorical constructions
Bordism and cobordism
Formal group laws and Hirzebruch genera
Bibliography
Index
MSRI Mathematical Circles Library, Volume: 16
2015; approx. 165 pp; softcover
ISBN-13: 978-0-8218-9416-3
Expected publication date is August 14, 2015.
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years.
This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments).
Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Undergraduate and graduate students and research mathematicians interested in mathematics.
Introduction
The statistics of topology and algebra
Combinatorial complexity and randomness
Random permutations of Young diagrams of their cycles
The geometry of Frobenius numbers for additive semigroups
Bibliography